Download Economic Concepts

Calculus
Chapter 3: Derivatives
B. Rates of change in physics and economics
1. Distance, Velocity, and Acceleration
The derivative of a function representing the position of a particle along a
line at time t is the instantaneous velocity at that time. The derivative of the
velocity, which is the second derivative of the position function, represents the
instantaneous acceleration of the particle at time t.
If y = s(t) represents the position function, then v = s′(t) represents the
instantaneous velocity, and a = v'(t) = s″(t) represents the instantaneous
acceleration of the particle at time t.
A positive velocity indicates that the position is increasing as time
increases, while a negative velocity indicates that the position is decreasing
with respect to time. If the distance remains constant, then the velocity will be
zero on such an interval of time. Likewise, a positive acceleration implies that
the velocity is increasing with respect to time, and a negative acceleration
implies that the velocity is decreasing with respect to time. If the velocity
remains constant on an interval of time, then the acceleration will be zero on
the interval.
Examples will be given in class.
2. Derivatives in economics
Economic Concepts
Marginal Quantities
The marginal cost is the change in total cost which results from producing one
additional unit. When the output is q, the marginal cost is
This is the slope of the line between the points
and
. The
derivative
,which is the slope of the tangent line at, gives a good
approximation to the exact change in cost, and it is customary to use the derivative
to compute the marginal cost.
The marginal revenue is the additional revenue derived from the sale of one
additional unit,
.
As with the cost function we will use the derivative of the revenue function to
determine marginal revenue.
The marginal profit is the additional profit derived from the sale of one
additional unit,
.
Again, we will use the derivative of the profit function to determine marginal
profit. Note that this is the difference between marginal revenue and marginal
cost,
Marginal Profit = Marginal Revenue - Marginal Cost.
Important Observation - If the profit function has a maximum, this occurs
when marginal revenue = marginal cost.
Examples will be given in class
Supply and Demand
A supply curve describes the relationship between the quantity supplied and the
selling price. The amount of a good or service that producers plan to sell at a given
price during a given period is called the quantity supplied. The quantity supplied is
the maximum amount that producers are willing to supply at a given price.
Quantity supplied is expressed as an amount per unit of time. For example, if a
producer plans to sell 750 units per day at $15 per unit we say that the quantity
supplied is 750 units per day at price $15.
Similarly, the amount of a good or service that consumers plan to buy at a
given price during a given period is called the quantity demanded. The quantity
demanded is the maximum amount that consumers can be expected to buy at a
given price, and it also is expressed as amount per unit of time.
The equilibrium price is the price at which the quantity demanded equals
the quantity supplied. The equilibrium quantity is the quantity bought and sold at
the equilibrium price. If the curves are graphed on the same coordinate system, the
point of intersection is the equilibrium point, and is where supply equals demand.
If the price is below equilibrium there will be a shortage and the price will rise,
while if the price is above equilibrium there will be a surplus and the price will
fall. If the price is at equilibrium it will stay there unless other factors enter to
cause changes.
Examples will be given in class